基于jitter采样和曲波变换的三维地震数据重建

Seismic data reconstruction based on jittered sampling and curvelet transform

传统的地震勘探数据采样必须遵循奈奎斯特采样定理,而野外数据采样可能由于地震道缺失或者勘探成本限制,不一定满足采样定理要求,因此存在数据重建问题.本文基于压缩感知理论,利用随机欠采样方法将传统规则欠采样所带来的互相干假频转化成较低幅度的不相干噪声,从而将数据重建问题转为更简单的去噪问题.在数据重建过程中引入凸集投影算法(POCS),提出采用e-(x^(1/2))(0≤x≤1)衰减规律的阈值参数,构建基于曲波变换三维地震数据重建技术.同时针对随机采样的不足,引入jitter采样方式,在保持随机采样优点的同时控制采样间隔.数值试验表明,基于曲波变换的重建效果优于傅里叶变换,jitter欠采样的重建效果优于随机欠采样,最后将该技术应用于实际地震勘探资料,获得较好的应用效果.

Traditional seismic data sampling must follow the Nyquist sampling theorem,while the field data acquisition can′t meet the sampling theorem due to missing traces or exploration cost limit,so there exits data reconstruction problem.In this paper,based on the theory of compressed sensing,we render coherent aliases of regular under-sampling into harmless incoherent random noise using the random under-sampling,effectively turning the reconstruction problem into a much simpler de-noising problem.We introduce the Projections Onto Convex Sets(POCS) algorithm during the process of reconstruction,choosing the square root exponentially decreased threshold,constructing a curvelet-based recovery strategy of 3D seismic data.At the same time,aiming at the deficiency of simple random under-sampling,we introduce the jittered under-sampling,it shares the benefits of random sampling and controls the maximum gap size.Experiments show that reconstruction effect based on curvelet is better than FFT transform and jittered under-sampling is better than random under-sampling.At last,we apply this technology into practical seismic data and obtain a good application.